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Phenomenon of bifurcation for nonlinear triharmonic equations

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2 Author(s)
Yang Jianhui ; Huazhong Univ. of Sci. & Technol., Wuhan, China ; H. O. Wang

In this paper, the problem of bifurcation of the triharmonic equation is discussed by the best embedding constant and Nhari-type variation method. The harmonic equation has at least two solutions and its solution has bifurcation. The biharmonic equation has at least a radial positive solution, but bifurcation of the solution can't be discovered. In triharmonic equation, the best embedding constant and Palais-Smale condition are given by the defined function, the triharmonic equation has at least a radial positive solution and a nonradial positive solution, bifurcation phenomenon can be discovered in the solution. We also supply method for discussing existence of solution of polyharmonic equation.

Published in:

Control, Automation, Robotics and Vision Conference, 2004. ICARCV 2004 8th  (Volume:3 )

Date of Conference:

6-9 Dec. 2004